Graphene-based materials (GBM) have outstanding properties that have proven highly beneficial in several proof-of-concept investigations on their biomedical potential. They can be used as suspensions of nanosheets for nanomedicine purposes as well as components of macroscale products in medical devices or tissue engineering/regenerative medicine products. However, the clinical translation of these preclinical concepts is hampered by the incomplete understanding of the biocompatibility of GBM in general, and the limited or lack of safety considerations in most preclinical proof-of-concept studies. In this review, the main safety aspects to be considered for the design of biocompatible materials based on GBM that interface with the human body or its fluids are outlined. Guidance to overcome some of the unique challenges presented by graphene biomedical materials are provided, stressing the need to consider safety challenges as early as possible in the design phase of the candidate biomedical product to raise its chance for clinical translation.